Question

1. A physical quantity P is related to four observables a, b and c as follows: P= (a3b 2 /c4 ) The percentage errors of measurements in a, b and c are 1%, 4% and 2% respectively. What is the percentage error in quantity P?

Answer 1

Answer:

The percentage error in quantity P is 19%.

Explanation:

It is given that,

A physical quantity P is related to four observables a, b and c as follows:

$P=\dfrac{a^3b^2}{c^4}$

The percentage errors of measurements in a, b and c are 1%, 4% and 2% respectively.

We need to find the percentage error in quantity P. It is given by :

$\dfrac{\Delta P}{P}\times 100=(3\times \dfrac{\Delta a}{a}+2\times \dfrac{\Delta b}{b}+4\times \dfrac{\Delta c}{c})\\\\=3\times 1+2\times 4+4\times 2\\\\\dfrac{\Delta P}{P}\times 100=19\%$

So, the percentage error in quantity P is 19%.